Question

Using these two equations a=(Mb-Ma)/(Mb+Ma)*g  and S = 1/2at^2, how can I find Mb? Is there any way to combine these two equations and derive them so I can solve for Mb? Your help is appreciated! (:

For my physics lab, I'm doing the atwood machine experiment and I was told I need to find Mb using these two equations but I dunno how to solve for Mb using these two equations. My Professor told me I have to derive them in order to find Mb.

Answer 1

Yes, it is possible to find , for this, we must have to know the value of the other variables.

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From the 2nd expression we have,

$S=\dfrac12at^2\\ a=\dfrac{S}{2t^2}$

Hence, expression one can be written as,

$a=\dfrac{M_b-M_a}{M_b+M_a}\\[.3 cm] \dfrac{S}{2t^2}= \dfrac{M_b-M_a}{M_b+M_a}\\[.3 cm] \dfrac{2t^2+S}{2t^2-S}= \dfrac{(M_b+M_a)+(M_b-M_a)}{(M_b+M_a)-(M_b-M_a)}\ \text{[Using componendo dividendo process]}\\[.3 cm] \dfrac{2t^2+S}{2t^2-S}=\dfrac{2M_b}{2M_a}\\[.3 cm]\dfrac{2t^2+S}{2t^2-S}=\dfrac{M_b}{M_a}\\[.3 cm]\color{red}{ M_b=\left [ \dfrac{2t^2+S}{2t^2-S} \right ]M_a}$This is the final expression for .

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